Numerical Analysis of Sample-Size Effect on Strength of Alumina

Statistical characteristics of strength distribution in ceramic components should be clarified because of large scatter in ceramics strength. Characteristics of strength distribution, however, depend on sample size, i.e., the number of tested specimens. In this study, a numerical procedure in the framework of fracture mechanics was developed to estimate strength distribution of ceramics by assuming the same statistical distribution of cracks in a material. Experimental results in four-point bending tests of alumina, which were reported in a previous work, were cited to verify the validity of the developed procedure. Smooth specimens of distinct sizes as well as notched specimens with different notch shapes were used in the experiment. Monte Carlo simulations using the developed procedure were carried out to investigate effects of the sample size on strength properties of alumina specimens with various shapes. The simulated result revealed that the experimental strength for various types of specimens was almost covered within a range of upper and lower bounds of strength simulated for the alumina. The experimental mean strength correlated with the effective volume was also included in a band range between the maximum and the minimum of mean strength obtained by the simulation.